spintronics -- materials aspectspintronics -- materials...
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Spintronics -- materials aspectSpintronics -- materials aspectWhy to do not combine complementary resources of
ferromagnets and semiconductors?
hybrid ferromagnetic-metal/semiconductor structures
TopGaN
cf. B. Dieny
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Hybrid structures – an example
(distributed non-volatile memory)
Adder: 34 MOSs + 4 MTJs S. Matsunaga et al.. (Tohoku) APEX’08
low-power hybrid logic
spintronics
electronics
cf. B. Dieny
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Spintronics -- materials aspectSpintronics -- materials aspectWhy to do not combine complementary resources of
ferromagnets and semiconductors?
TopGaN
ferromagnetic semiconductors – multifunctional materials
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• Antiferromagnetic superexchange dominatesin magnetic insulators and semiconductors
no spontaneous magnetisationNiO, MnSe, EuTe, …
Search for ferromagnetic semiconductors
Mn Se Mn
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• Antiferromagnetic superexchange dominatesin magnetic insulators and semiconductors
no spontaneous magnetisationNiO, MnSe, EuTe, …
• Exceptions-- ferromagnetic superexchange dominates
EuO, ZnCr2Se4, … TC ≈ 100 K IBM, MIT, Tohoku, … ‘60-’70
-- double exchange (two charge states co-exist)LaMnO3 La1-xSrxMnO3 (holes in d band)
-- ferrimagnets (two ions or two spin states co-exist)Mn4N, NiO(Fe2O3), …
Search for ferromagnetic semiconductors
Mn+3 Mn+4
Mn Se Mn
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Spintronics -- materials aspectSpintronics -- materials aspectWhy to do not combine complementary resources of
ferromagnets and semiconductors?
TopGaN
ferromagnetic semiconductors – multifunctional materials
• making good semiconductors of magnetic oxides
• making good semiconductors magneticR.R. Gałązka et al. (Warsaw)’77- ; H. Ohno et al. (IBM, Tohoku) ’89 -
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• Intrinsic DMS – random antiferromagnetsCd1-xMnxTeZn1-xCoxO
Making DMS ferromagnetic
laser CdMnTemagnet
fiber
optical isolator TOKINB
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• Intrinsic DMS – random antiferromagnetsCd1-xMnxTeZn1-xCoxO
Making DMS ferromagnetic
laser CdMnTemagnet
fiber
optical isolator TOKINB
• p+-type DMS - ferromagnets
IV-VI: p-Pb1-x-y-MnxSnyTe Story et al. (Warsaw, MIT) PRL’86p-Ge1-xMnxTe
III-V: In1-x-MnxAs Ohno et al. (IBM) PRL’92
Ga1-x-MnxAs Ohno et al. (Tohoku) APL’96
II-VI: Cd1-xMnxTe/Cd1-x-yZnxMgyTe:N QW Haury et al.(Grenoble,Warsaw) PRL’97
Zn1-xMnxTe:N Ferrand et al. (Grenoble, Linz, Warsaw) Physica B’99, PRB’01
TC ≈ 110 K for x = 0.05
Lechner et al. (Linz))
quantum nanostructures and ferromagnetism combined
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Transport in magnetic semiconductors and oxides
Tomasz Dietl
1. Institute of Physics, Polish Academy of Sciences, Laboratory for Cryogenic and Spintronic Research
2. Institute of Theoretical Physics, Warsaw University
support: FunDMS – ERC Advanced GrantSemiSpinNet Maria Curie actionSPINTRA – ESF; Humboldt Foundation
Lecture 4
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Dual character of description of carriers in solidsDual character of description of carriers in solids
I. Carriers reside in c/v band-- Boltzmann conductivity:
1/τ = 1/τii + 1/τph(T) + …σ(T) σo > 0; ρ(T) ρo < ∞ for T 0
-- dielectric functionε(q) ∞ for q 0
-- electron-electron interactionunimportant
-- ….
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II. Carriers reside on impuritiesII. Carriers reside on impurities
-- phonon-assisted hoppingσ(T) 0; ρ(T) ∞ for T 0
-- dielectric functionε(q) εs < ∞ for q 0
-- electron-electron interaction important(Coulomb gap in DOS, …)
-- ….
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Extended vs. localized statesExtended vs. localized states
Sensitive to boundaryconditions
Insensitive to boundaryconditions
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Examples of metal-insulatortransition (MIT)
cf. J. Spałek
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MIT in doped semiconductorsMIT in doped semiconductors
Jaroszynski … T.D..’83
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MIT in various materialsMIT in various materials
For hydrogenic-like donors:aB
* = aB εs/(m*/mo)
More general:aB
* = ħ/(2EIm*)1/2
*
rs/aB* = [3/(4πnc)1/3]/aB ≈ 2.5
Edwards, Sienko (Cornell) PRB’78
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Wojtowicz … TDPRL’86
MIT in p-(Hg,Mn)Te -- disorder (scattering by Mnspins) reduced by the magnetic field
MIT in p-(Hg,Mn)Te -- disorder (scattering by Mnspins) reduced by the magnetic field
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Spin/charge transport on the metallic side of the Anderson-
Mott MIT
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p-d Zener model of hole-mediated ferromagnetism in DMS
Driving force: lowering of the hole energy due to redistribution between hole spin subbands split by p-d exchange interaction, Δ ~ βM
T.D. et al.,’97-MacDonald et al. (Austin/Prague) ’99-
No adjustable parametersTC ~ β2ρ(s)
DOS
Essential ingredient: Complexity of the valence band structurehas to be taken into account
M
k
EF
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p-d Zener model + Luttinger-Kohn kp theory of carrier-mediated ferromagnetism in DMS
• p-d Zener model + 6x6 (or 8x8) kp theory describes quantitatively or semi-quantitatively:-- thermodynamic [TC, M(T,H)]
-- micromagnetic
(magnetic anisotropy, magnetic stiffness, magnetic domains)
-- dc and ac charge and spin transport
(AHE, AMR, PHE, σ(ω), ESR)
-- optical properties (MCD)Warsaw/Tohoku 1999-, Austin/Prague 2001-
bases for magnetization manipulationTohoku/ Warsaw/Grenoble/Wuerzburg/Orsay/Hitachi/Prague
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a recent example
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Spin Esaki-Zener Diode
Spin Esaki-Zener diode
Recent experimental results: Polarization of electrons Pj up to 70%
How to change spin polarization of holes into spin polarized electrons
Tohoku, St. Barbara, IMEC, Regensburg,...
σ +
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Description of spin transport effects in ferromagnetic structures
• two spin channels characterized by f↑ and f↓-- spin diffusion equation-- continuity conditions-- boundary conditions
Aronov et al. ’76-- ; Silsbee et al. ’80-- ; Fert et al. ’93-- , Schmidt et al. ’00—
spin accumulation, resistance mismatch, ...cf. B. Dieny
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Description of spin transport effects in ferromagnetic structures
• two spin channels characterized by f↑ and f↓-- spin diffusion equation-- continuity conditions-- boundary conditions
Aronov et al. ’76-- ; Silsbee et al. ’80-- ; Fert et al. ’93-- , Schmidt et al. ’00—
spin accumulation, resistance mismatch, ...
-- Implicit assumption: Ls >> Lϕ
is it valid in (Ga,Mn)As?
cf. B. Dieny
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(Ga,Mn)As: universal conductance fluctuations
Kawabata’80
Wagner et al. (Regensburg) PRL’06 Vila et al. (Marcoussis, Grenoble) PRL’07
Lϕ(T) ≈ 100 nm at 4 K from WLR and UCF
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Description of spin transport in modulated structuresof (Ga,Mn)As
• in (Ga,Mn)As type materials:-- four channels strongly mixed by spin-orbit interaction
Ls ≤ Lϕ(T) ≈ 30 nm at 4 K from WLR and UCF
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Description of spin transport in modulated structures of (Ga,Mn)As
• in (Ga,Mn)As type materials:-- four channels strongly mixed by spin-orbit interaction
Ls ≤ Lϕ(T) ≈ 30 nm at 4 K from WLR and UCF
quantum Landauer-Buettiker formalismimplementation for semiconductor layered structures, see A. Di Carlo, SST’03
-- uniform and infinite in 2D (kx, ky good quantum numbers)
-- modulation in 1D
-- simulation length L ≈ Lϕ
L = Lϕ
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Description of semiconductor band structure
kp method: RTD Petukhov et al., PRL’02
TMR Brey, APL’04, Jeffres ‘06
DWR Nguyen et al., PRL’06
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Description of semiconductor band structure
kp method: RTD Petukhov et al., PRL’02
TMR Brey, APL’04, Jeffres ‘06
DWR Nguyen et al., PRL’06
Standard kp formalism disregards effectsimportant for spin transport and spin tunneling:
• Rashba and Dresselhaus terms
• spin filtering at interfaces cf. Fe/MgO
• spin-mixing conductance Brataas et al. ’01
• band extrema away from the center of the Brillouin zone
These can be taken into account within empirical tight-binding approach
cf. A. Bonanni
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Tight-binding model
GaAs: sp3d5s*:nn coupling
Ga and As atoms: 20 orbitals
parametrization: M.-J. Jancu et al., PRB’98
(Ga,Mn)As: GaAs + spin splittingVCA, MFA
Δc = αNox<Sz>, Δ v = βNox<Sz>,
αNo = 0.2 eV, βNo = -1.2 eV
no adjustable parameters
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Landauer-Büttiker + tight-binding model for (Ga,Mn)As-based structures -- summary
• The model describes-- magnitude and anisotropy of Pj and TMR-- decay of Pj and TMR with V-- crystalline anisotropy of Pj and TMR
P. Sankowski… T.D., PRB’05, 07
• LLG eq. + adiabatic spin torque describes:-- current-induced domain-wall velocity
D. Chiba… T.D. … PRL’06
• The model does not describe:-- domain-wall resistance disorder essential
R. Oszwaldowski … T.D. PRB’06
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Spin/charge transport near the Anderson-Mott MIT
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Ga1-xMnxAs: resistance vs. temperature and Curie temperature vs. x
Ga1-xMnxAs: resistance vs. temperature and Curie temperature vs. x
• ferromagnetism on both sides of metal-insulator transitions• ferromagnetism disappears in the absence of holes
0 100 200 300
10-2
10-1
100
101
INSULATOR
METAL
x0.0150.0220.0710.0350.0430.053
RE
SIS
TIV
ITY
(Ωcm
)
TEMPERATURE (K)
0.00 0.04 0.080
40
80
120
T c (K)
x
F. Matsukura et al. (Tohoku) PRB’98
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Ferromagnetic temperature in p-(Zn,Mn)TeFerromagnetic temperature in p-(Zn,Mn)Te
D. Ferrand et al. (Grenoble, Warsaw) PRB’01M. Sawicki et al. (Warsaw) pss’02
1
10
1
10
3030Fe
rrom
agne
tic T
emp.
TF
/ xef
f(K
) 1017 1018 1019 10205x1020
Hole concentration (cm-3)
(Zn ,Mn )Te:P
( Zn ,Mn )Te:N
InsulatingMetallic
• ferromagnetism disappears in the absence of holes• ferromagnetism on both sides of metal-insulator transition
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Conductance vs. bias in a TMR structure of (Ga,Mn)As- evidence for a Coulomb gap and TAMR
Conductance vs. bias in a TMR structure of (Ga,Mn)As- evidence for a Coulomb gap and TAMR
Pappert et al. (Wuerzburg) PRL’06
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(Classical) percolationtheory of MIT
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Conductive/nonconductive compositesConductive/nonconductive composites
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(Quantum) Anderson localization
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Particle/wave propagation in solidsParticle/wave propagation in solidsCrystals (periodic potential)
Classical particles: channeling(e.g., Rutherford back scattering of α particles)
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Particle/wave propagation in solidsParticle/wave propagation in solidsCrystals (periodic potential)
Classical particles: channeling(e.g., Rutherford back scattering of α particles)
Quantum particles: (electrons, photons,...)Energy bands: quasi-free (ballistic) propagationEnergy gaps: regions of evanescent waves
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Particle/wave propagation in solidsParticle/wave propagation in solidsCrystals (periodic potential)
Classical particles: channeling(e.g., Rutherford back scattering of α particles)
Quantum particles: (electrons, photons,...)Energy bands: quasi-free (ballistic) propagationEnergy gaps: regions of evanescent waves
Disordered solids Classical particles:diffusion above percolation threshold
2 1 / 2( ( ) ) 2r t t D d< > = ∞ for t ∞
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Anderson localizationAnderson localizationQuantum localization by scattering
V(r)
Lc
r
electron energy E
Occurs even if E > Vmax
1. Contradicts classical percolation picture
2. Contradicts classical diffusion equation2 1 / 2( ( ) ) 2r t tD d< > = ∞ for t ∞
Cannot be described by CPA,…
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Enhanced backscatteringEnhanced backscattering
0
Amplitude of scattered wave
Experimental evidence for backscattering:oscillations in rings and magnetoresistance in films
Treturn = Tr + Tl + 2|TrTl|1/2cos(ϕr - ϕl)
ϕr - ϕl = 0 if no magnetic field and spin scatteringFactor of two enhancement over classical value
ϕr = ϕi
Khmelnitskii, Larkin, Hikami, ….
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Enhanced backscatteringEnhanced backscattering
0
Amplitude of scattered wave
Treturn = Tr + Tl + 2|TrTl|1/2cos(ϕr - ϕl)
ϕr - ϕl = 0 if no magnetic field and inelastic scatteringFactor of two enhancement over classical value
magnetic field and temperature enhance diffusion
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Quantum localisation magnetoresistancein n-wz ZnO
Quantum localisation magnetoresistancein n-wz ZnO
T. Andrearczyk, …, T.D., PRB’05
λso[meVÅ] CdSe ZnO
WLR 50±10 4.4±0.4
LMTO-LSD* 30 2.2 *Voon et al. (Stuttgart, Aarhus) PRB’96Dyakonov-Perel; Fukuyama, Hoshino
T2 = 10 nsHso = λsoĉ(s×k)τsox
-1 = λso2kF
2τ /12Bm ≈ 1.6 αso
2m*2
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(Ga,Mn)As: low temperature negativemagnetoresistance
A. Kawabata’80
F. Matsukura … T.D. (Warsaw, Tohoku)’04
theory
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(Ga,Mn)As: low temperature negativemagnetoresistance
A. Kawabata’80
F. Matsukura … T.D. (Warsaw, Tohoku)’04
theory
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Electron-electron scatteringElectron-electron scattering
clean systemsballistic motion:
electrons never meet again…
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Electron-electron scatteringElectron-electron scattering
clean systemsballistic motion:
electrons never meet again…
disordered systemsdiffusive motion:
electrons can meet again…
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Electron-electron scatteringElectron-electron scattering
interference of scattering amplitudesTσσ’ = Tσ + Tσ ‘+ 2|TσTσ’|1/2cos(ϕσ - ϕσ’)
depending of spins (triplet vs. singlet):diffusion reduced/enhancedCoulomb anomaly at EF
clean systemsballistic motion:
electrons never meet again…
disordered systemsdiffusive motion:
electrons can meet again…
Altshuler, Aronov, Fukuyama, Lee, Ramakrishnan, …
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Electron-electron scatteringElectron-electron scattering
interference of scattering amplitudesTσσ’ = Tσ + Tσ ‘+ 2|TσTσ’|1/2cos(ϕσ - ϕσ’)
same spins: diffusion reducedopposite spins: diffusion enhances
spin splitting and spin scattering reduce diffusion
clean systemsballistic motion:
electrons never meet again…
disordered systemsdiffusive motion:
electrons can meet again…
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4000
5000
6000
7000
8000
9000
0.01 0.1 1 10 100 1000
8
7
6
5
4
3
2
1
0
T [K]
sigX
X [1
/ohm
/m]
matsu I || [010]
B[T]
Temperature dependence of conductance invarious magnetic fields in (Ga,Mn)As
x = 0.04
F. Matsukura et al. (Warsaw, Tohoku)’04,’05, D. Neumaier et al. (Regensburg)’ 08’09
Temperature (K)
σ xx(
Sm
-1)
σ = σo + mT1/2
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we do not understand
• critical scattering at TC( at T 0 in paramagnets)
• CMR
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4000
5000
6000
7000
8000
9000
0.01 0.1 1 10 100 1000
8
7
6
5
4
3
2
1
0
T [K]
sigX
X [1
/ohm
/m]
matsu I || [010]
B[T]
Temperature dependence of conductivity invarious magnetic fields in (Ga,Mn)As
x = 0.04
F. Matsukura …T. D. (Warsaw, Tohoku)’04,’05, Neumaier et al. (Regensburg)’,08
Temperature (K)
σ xx(
Sm
-1)
σ = σo + mT1/2
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Temperature dependence of resistivity invarious magnetic fields in (Ga,Mn)As
F. Matsukura et al., PRB’98
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Temperature dependence of resistivity invarious magnetic fields in (Ga,Mn)As
F. Matsukura et al., PRB’98Reminiscent to CMR oxides
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Magnetization and resistivity in (La,Ca)MnO3
P. Schiffer et al. (PSU), PRL’95
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Phase diagram of La1-xCaxMnO3
CMR near MIT
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CMR in n-(Cd,Mn)Se
M. Sawicki, TD et al. (Warsaw) PRL’86, Physica B’93
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Possible model: enhancement of localization by bound magnetic polaron formation
p-type(II,Mn)VI
(III,Mn)V
BMP binding energy ~ χ(T)
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Resistivity vs. carrier density at various Tin (Cd,Mn)Te/(Cd,Mg)Te:I quantum well
Electron density (cm-2)J. Jaroszynski , TD et al.
(Warsaw, NHMFL) PRB’07
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Resistivity vs. carrier density at various Tin (Cd,Mn)Te/(Cd,Mg)Te:I quantum well
J. Jaroszynski , TD et al. (Warsaw, NHMFL) PRB’07
no BMP but criticalscattering and CMR!
Electron density (cm-2)
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Pictorial representation of states near MIT
white = para grey = ferro (mesoscopic scale)
cf. A. Moreo et al.Science’99Nagaev’85
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Nanoscale electronic phase separation
TC > 0 in p-type DMS
TC ≅ 0 in
n-type DMS
strong-spin dependent scatteringand CMR
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SUMMARY
Quantum effects essential at the Anderson-Mott transition
Leads to:
• Coulomb anomaly of DOS at EF
• specific dependence σ(T,H)
• nanoscale phase separation into para and ferro regions
colossal negative magnetoresistance
much enhanced critical scattering
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END